Data for Study 1 was collected in Fall 2015. Data for Study 2 was collected in Fall 2016.
In Study 1:
- 101 subjects participated
- 8 subjects’ AP data was discarded (see “Study1_badsubsAP.txt”)
- 9 subjects’ WIT data was discarded (see “Study1_badsubsWIT.txt”)
This left 93 subjects with AP data and 92 subjects with WIT data.
Additionally, IMS/EMS data is missing for subs 3, 27, 53, 82, 88, 89, 90, and 101.
In Study 2:
- 206 subjects participated
- 8 subjects’ AP data was discarded (see “Study2_badsubsAP.txt”)
- 7 subjects’ WIT data was discarded (see “Study2_badsubsWIT.txt”)
This left 198 subjects with AP data and 199 subjects with WIT data.
Additionally, IMS/EMS data is missing for 111, 189, and 201.
There were 48 trials for each condition in each task. In Study 2, each task was split into two sections so that participants could answer anxiety questions in the middle and end of each task.
Only showing interaction indicating racial bias (Prime x Target). For calculation of effect sizes, see “7 Effect sizes.R”
#### Study 1:
WIT
## Df Sum Sq Mean Sq F value Pr(>F)
## PrimeType:TargetType 1 2883 2882.9 96.5 5.97e-16 ***
## Residuals 91 2719 29.9
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
AP
## Df Sum Sq Mean Sq F value Pr(>F)
## PrimeType:TargetType 1 1794 1794.3 39.82 9.63e-09 ***
## Residuals 92 4145 45.1
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Only showing interaction indicating racial bias (Prime x Target). For calculation of effect sizes, see “7 Effect sizes.R”
WIT
## Df Sum Sq Mean Sq F value Pr(>F)
## PrimeType:TargetType 1 3861 3861 120.7 <2e-16 ***
## Residuals 198 6331 32
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
AP
## Df Sum Sq Mean Sq F value Pr(>F)
## PrimeType:TargetType 1 2478 2478.3 54.86 3.71e-12 ***
## Residuals 197 8900 45.2
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Excludes subjects that don’t have data in both tasks (only includes sample of 90).
##
## Call:
## lm(formula = APStand ~ WITStand, data = s1.perfBias)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.25273 -0.64697 -0.04138 0.68037 2.40625
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9.621e-17 1.042e-01 0.000 1.0000
## WITStand 1.851e-01 1.048e-01 1.767 0.0807 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9883 on 88 degrees of freedom
## Multiple R-squared: 0.03427, Adjusted R-squared: 0.02329
## F-statistic: 3.123 on 1 and 88 DF, p-value: 0.08068
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## Df Sum Sq Mean Sq F value Pr(>F)
## PrimeType:ConType:Task 1 992 991.7 23.04 6.35e-06 ***
## Residuals 89 3830 43.0
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Excludes subjects that don’t have data in both tasks (only includes sample of 195).
##
## Call:
## lm(formula = APStand ~ WITStand, data = s2.perfBias)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.1856 -0.6008 -0.0491 0.5380 4.4047
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.394e-16 6.594e-02 0.000 1
## WITStand 4.065e-01 6.611e-02 6.149 4.46e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.916 on 191 degrees of freedom
## Multiple R-squared: 0.1653, Adjusted R-squared: 0.1609
## F-statistic: 37.82 on 1 and 191 DF, p-value: 4.456e-09
## Saving 7 x 5 in image
## Df Sum Sq Mean Sq F value Pr(>F)
## PrimeType:ConType:Task 1 3123 3123.3 94.02 <2e-16 ***
## Residuals 192 6378 33.2
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Call:
## lm(formula = WIT_MeanC.stand ~ AP_MeanC.stand, data = s1.widePDP)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.77991 -0.52543 0.04554 0.59056 1.68756
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.088e-16 8.353e-02 0.000 1
## AP_MeanC.stand 6.157e-01 8.400e-02 7.329 1.06e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7925 on 88 degrees of freedom
## Multiple R-squared: 0.379, Adjusted R-squared: 0.372
## F-statistic: 53.72 on 1 and 88 DF, p-value: 1.062e-10
##
## Call:
## lm(formula = WIT_AResid.stand ~ AP_AResid.stand, data = s1.widePDP)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.64807 -0.47586 0.03648 0.71495 2.42030
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9.771e-17 1.030e-01 0.000 1.0000
## AP_AResid.stand 2.349e-01 1.036e-01 2.267 0.0258 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9775 on 88 degrees of freedom
## Multiple R-squared: 0.05519, Adjusted R-squared: 0.04445
## F-statistic: 5.14 on 1 and 88 DF, p-value: 0.02583
## Saving 7 x 5 in image
##
## Call:
## lm(formula = WITestimate ~ APTestimate * Type, data = compareAC)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.64807 -0.49558 0.03792 0.65228 2.42030
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.629e-16 9.380e-02 0.000 1.00000
## APTestimate 2.349e-01 9.432e-02 2.491 0.01368 *
## TypePDP-C 5.879e-16 1.326e-01 0.000 1.00000
## APTestimate:TypePDP-C 3.807e-01 1.334e-01 2.854 0.00483 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8898 on 176 degrees of freedom
## Multiple R-squared: 0.2171, Adjusted R-squared: 0.2038
## F-statistic: 16.27 on 3 and 176 DF, p-value: 2.233e-09
##
## Call:
## lm(formula = WIT_MeanC.stand ~ AP_MeanC.stand, data = s2.widePDP)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.79597 -0.54572 0.03667 0.51197 1.86599
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.645e-16 5.468e-02 0.00 1
## AP_MeanC.stand 6.527e-01 5.482e-02 11.91 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7596 on 191 degrees of freedom
## Multiple R-squared: 0.426, Adjusted R-squared: 0.423
## F-statistic: 141.7 on 1 and 191 DF, p-value: < 2.2e-16
##
## Call:
## lm(formula = WIT_AResid.stand ~ AP_AResid.stand, data = s2.widePDP)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.3346 -0.6315 -0.0074 0.6270 2.3417
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.869e-17 6.973e-02 0.000 1.000000
## AP_AResid.stand 2.577e-01 6.991e-02 3.685 0.000298 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9688 on 191 degrees of freedom
## Multiple R-squared: 0.06639, Adjusted R-squared: 0.0615
## F-statistic: 13.58 on 1 and 191 DF, p-value: 0.0002975
## Saving 7 x 5 in image
##
## Call:
## lm(formula = WITestimate ~ APTestimate * Type, data = compareAC)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.33459 -0.57549 0.01939 0.57615 2.34165
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.660e-17 6.266e-02 0.000 1
## APTestimate 2.577e-01 6.282e-02 4.101 5.02e-05 ***
## TypePDP-C -2.384e-16 8.861e-02 0.000 1
## APTestimate:TypePDP-C 3.950e-01 8.884e-02 4.446 1.15e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8705 on 382 degrees of freedom
## Multiple R-squared: 0.2462, Adjusted R-squared: 0.2403
## F-statistic: 41.59 on 3 and 382 DF, p-value: < 2.2e-16
Perf bias:
## Df Sum Sq Mean Sq F value Pr(>F)
## Observer 1 0.0007 0.000738 0.045 0.833
## Residuals 178 2.9422 0.016529
Effect size (eta-squared) is 0.
PDP-A estimates:
## Df Sum Sq Mean Sq F value Pr(>F)
## Observer 1 0.011 0.01090 0.462 0.498
## Residuals 178 4.205 0.02363
Effect size (eta-squared) is 0.003.
PDP-C estimates:
## Df Sum Sq Mean Sq F value Pr(>F)
## Observer 1 0.013 0.01285 0.315 0.576
## Residuals 178 7.272 0.04085
Effect size (eta-squared) is 0.002.
Anxiety composite:
## Df Sum Sq Mean Sq F value Pr(>F)
## Observer 1 0.06 0.0617 0.041 0.839
## Residuals 178 266.90 1.4994
Effect size (eta-squared) is 0.
Perf bias:
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | 0.0606414 | 0.0131239 | 4.6206923 | 0.0000053 |
| scale(IMS) | -0.0090080 | 0.0124408 | -0.7240669 | 0.4694798 |
| ObserverPresent | 0.0332584 | 0.0190066 | 1.7498343 | 0.0809714 |
| TaskWIT | 0.0355513 | 0.0185600 | 1.9154856 | 0.0561970 |
| scale(IMS):ObserverPresent | -0.0159428 | 0.0192768 | -0.8270496 | 0.4087391 |
| scale(IMS):TaskWIT | -0.0101322 | 0.0175940 | -0.5758906 | 0.5650373 |
| ObserverPresent:TaskWIT | -0.0413698 | 0.0268794 | -1.5390890 | 0.1246327 |
| scale(IMS):ObserverPresent:TaskWIT | 0.0277632 | 0.0272615 | 1.0184042 | 0.3091478 |
PDP-C estimates:
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | 0.3355554 | 0.0233887 | 14.3468823 | 0.0000000 |
| scale(IMS) | 0.0402489 | 0.0221714 | 1.8153523 | 0.0702749 |
| ObserverPresent | -0.0003638 | 0.0338727 | -0.0107404 | 0.9914363 |
| TaskWIT | 0.0595237 | 0.0330767 | 1.7995666 | 0.0727393 |
| scale(IMS):ObserverPresent | -0.0049051 | 0.0343541 | -0.1427815 | 0.8865400 |
| scale(IMS):TaskWIT | -0.0110335 | 0.0313551 | -0.3518874 | 0.7251219 |
| ObserverPresent:TaskWIT | 0.0228862 | 0.0479032 | 0.4777597 | 0.6331019 |
| scale(IMS):ObserverPresent:TaskWIT | -0.0113101 | 0.0485841 | -0.2327951 | 0.8160485 |
PDP-A estimates:
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | 0.0102392 | 0.0154690 | 0.6619198 | 0.5084324 |
| scale(IMS) | -0.0273694 | 0.0146638 | -1.8664580 | 0.0627639 |
| ObserverPresent | -0.0215384 | 0.0224029 | -0.9614123 | 0.3369694 |
| TaskWIT | -0.0081381 | 0.0218764 | -0.3720030 | 0.7101024 |
| scale(IMS):ObserverPresent | 0.0122012 | 0.0227213 | 0.5369929 | 0.5915935 |
| scale(IMS):TaskWIT | -0.0012590 | 0.0207378 | -0.0607111 | 0.9516219 |
| ObserverPresent:TaskWIT | 0.0176881 | 0.0316825 | 0.5582936 | 0.5769798 |
| scale(IMS):ObserverPresent:TaskWIT | -0.0149861 | 0.0321328 | -0.4663816 | 0.6412154 |
Composite is composed of 8 items (standardized before averaged together), alpha = .91
Look at correlation between first and second blocks:
The correlation between the anxiety composite score on the first block and the second block is 0.9098042.
Anxiety composite scores were averaged across blocks, so each participant has one anxiety score per task.
## Saving 7 x 5 in image
## Linear mixed model fit by REML
## t-tests use Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: MeanC ~ scale(Anx_composite) * Task + (1 | Subject)
## Data: s2.wide
##
## REML criterion at convergence: -136.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.09061 -0.49271 0.03496 0.55697 1.95890
##
## Random effects:
## Groups Name Variance Std.Dev.
## Subject (Intercept) 0.03381 0.1839
## Residual 0.01764 0.1328
## Number of obs: 386, groups: Subject, 193
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.33925 0.01633 266.70000 20.769 < 2e-16 ***
## scale(Anx_composite) -0.04235 0.01469 377.00000 -2.884 0.00415 **
## TaskWIT 0.06763 0.01355 191.20000 4.991 1.35e-06 ***
## scale(Anx_composite):TaskWIT -0.02641 0.01399 196.70000 -1.889 0.06043 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) sc(A_) TskWIT
## scl(Anx_cm) -0.031
## TaskWIT -0.415 0.058
## sc(A_):TWIT 0.014 -0.455 0.002
## Saving 7 x 5 in image
## Linear mixed model fit by REML
## t-tests use Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: AResid ~ scale(Anx_composite) * Task + (1 | Subject)
## Data: s2.wide
##
## REML criterion at convergence: -331.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.36687 -0.65794 -0.04769 0.60500 2.60405
##
## Random effects:
## Groups Name Variance Std.Dev.
## Subject (Intercept) 0.005595 0.0748
## Residual 0.018353 0.1355
## Number of obs: 386, groups: Subject, 193
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -4.377e-04 1.115e-02 3.622e+02 -0.039 0.969
## scale(Anx_composite) 1.421e-02 1.096e-02 3.786e+02 1.296 0.196
## TaskWIT 3.064e-03 1.380e-02 1.912e+02 0.222 0.825
## scale(Anx_composite):TaskWIT 1.089e-02 1.403e-02 2.104e+02 0.776 0.438
##
## Correlation of Fixed Effects:
## (Intr) sc(A_) TskWIT
## scl(Anx_cm) -0.033
## TaskWIT -0.619 0.032
## sc(A_):TWIT 0.021 -0.624 0.001
## Warning: Removed 6 rows containing non-finite values (stat_smooth).
## Warning: Removed 6 rows containing missing values (geom_point).
## Warning: Removed 6 rows containing non-finite values (stat_smooth).
## Warning: Removed 6 rows containing missing values (geom_point).
## Linear mixed model fit by REML
## t-tests use Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: scale(Anx_composite) ~ scale(IMS) * Observer * Task + (1 | Subject)
## Data: s2.wide
##
## REML criterion at convergence: 853.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.16647 -0.41242 -0.03104 0.41614 2.71661
##
## Random effects:
## Groups Name Variance Std.Dev.
## Subject (Intercept) 0.8195 0.9053
## Residual 0.1543 0.3929
## Number of obs: 380, groups: Subject, 190
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.05536 0.10002 217.78000 0.554 0.580487
## scale(IMS) 0.32910 0.09481 217.78000 3.471 0.000625 ***
## ObserverPresent 0.01621 0.14485 217.78000 0.112 0.910999
## TaskWIT -0.06212 0.05631 186.00000 -1.103 0.271398
## scale(IMS):ObserverPresent -0.29884 0.14691 217.78000 -2.034 0.043146 *
## scale(IMS):TaskWIT -0.12604 0.05338 186.00000 -2.361 0.019257 *
## ObserverPresent:TaskWIT -0.03449 0.08155 186.00000 -0.423 0.672846
## scale(IMS):ObserverPresent:TaskWIT 0.15425 0.08271 186.00000 1.865 0.063769 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) sc(IMS) ObsrvP TskWIT sc(IMS):OP s(IMS):T OP:TWI
## scale(IMS) 0.129
## ObsrvrPrsnt -0.690 -0.089
## TaskWIT -0.282 -0.036 0.194
## scl(IMS):OP -0.083 -0.645 -0.030 0.023
## s(IMS):TWIT -0.036 -0.282 0.025 0.129 0.182
## ObsrvP:TWIT 0.194 0.025 -0.282 -0.690 0.008 -0.089
## s(IMS):OP:T 0.023 0.182 0.008 -0.083 -0.282 -0.645 -0.030
## Warning: Removed 6 rows containing non-finite values (stat_smooth).
## Warning: Removed 6 rows containing missing values (geom_point).
## Warning: Removed 6 rows containing non-finite values (stat_smooth).
## Warning: Removed 6 rows containing missing values (geom_point).
## Linear mixed model fit by REML
## t-tests use Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: scale(Anx_composite) ~ scale(EMS) * Observer * Task + (1 | Subject)
## Data: s2.wide
##
## REML criterion at convergence: 850.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.27546 -0.40978 -0.01832 0.44454 2.53021
##
## Random effects:
## Groups Name Variance Std.Dev.
## Subject (Intercept) 0.7796 0.8830
## Residual 0.1591 0.3988
## Number of obs: 380, groups: Subject, 190
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.008509 0.097376 220.150000 0.087 0.930449
## scale(EMS) 0.343958 0.102343 220.150000 3.361 0.000916 ***
## ObserverPresent 0.068828 0.140705 220.150000 0.489 0.625210
## TaskWIT -0.045014 0.056690 186.000000 -0.794 0.428180
## scale(EMS):ObserverPresent -0.142602 0.140972 220.150000 -1.012 0.312859
## scale(EMS):TaskWIT 0.011562 0.059581 186.000000 0.194 0.846342
## ObserverPresent:TaskWIT -0.047481 0.081914 186.000000 -0.580 0.562855
## scale(EMS):ObserverPresent:TaskWIT -0.022435 0.082070 186.000000 -0.273 0.784873
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) sc(EMS) ObsrvP TskWIT sc(EMS):OP s(EMS):T OP:TWI
## scale(EMS) -0.006
## ObsrvrPrsnt -0.692 0.004
## TaskWIT -0.291 0.002 0.201
## scl(EMS):OP 0.004 -0.726 0.000 -0.001
## s(EMS):TWIT 0.002 -0.291 -0.001 -0.006 0.211
## ObsrvP:TWIT 0.201 -0.001 -0.291 -0.692 0.000 0.004
## s(EMS):OP:T -0.001 0.211 0.000 0.004 -0.291 -0.726 0.000
## Warning: Removed 6 rows containing non-finite values (stat_smooth).
## Warning: Removed 6 rows containing missing values (geom_point).
## Linear mixed model fit by REML
## t-tests use Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: scale(Anx_composite) ~ scale(IMS.EMS.diff) * Observer * Task + (1 | Subject)
## Data: s2.wide
##
## REML criterion at convergence: 862.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.1945 -0.4221 -0.0138 0.4133 2.5022
##
## Random effects:
## Groups Name Variance Std.Dev.
## Subject (Intercept) 0.8482 0.921
## Residual 0.1568 0.396
## Number of obs: 380, groups: Subject, 190
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.008219 0.101134 217.250000 0.081 0.935
## scale(IMS.EMS.diff) -0.027382 0.103972 217.250000 -0.263 0.793
## ObserverPresent 0.081193 0.146152 217.250000 0.556 0.579
## TaskWIT -0.052872 0.056492 186.000000 -0.936 0.351
## scale(IMS.EMS.diff):ObserverPresent -0.118671 0.146224 217.250000 -0.812 0.418
## scale(IMS.EMS.diff):TaskWIT -0.094283 0.058077 186.000000 -1.623 0.106
## ObserverPresent:TaskWIT -0.041573 0.081638 186.000000 -0.509 0.611
## scale(IMS.EMS.diff):ObserverPresent:TaskWIT 0.116359 0.081678 186.000000 1.425 0.156
##
## Correlation of Fixed Effects:
## (Intr) sc(IMS.EMS.) ObsrvP TskWIT sc(IMS.EMS.):OP s(IMS.EMS.):T OP:TWI
## sc(IMS.EMS.) 0.086
## ObsrvrPrsnt -0.692 -0.060
## TaskWIT -0.279 -0.024 0.193
## sc(IMS.EMS.):OP -0.061 -0.711 -0.003 0.017
## s(IMS.EMS.):T -0.024 -0.279 0.017 0.086 0.199
## ObsrvP:TWIT 0.193 0.017 -0.279 -0.692 0.001 -0.060
## s(IMS.EMS.):OP: 0.017 0.199 0.001 -0.061 -0.279 -0.711 -0.003